September 2017 Update

Task/Arithmetic-Complex/Jq/arithmetic-complex-1.jq

@@ -0,0 +1,62 @@
+def real(z): if (z|type) == "number" then z else z[0] end;
+
+def imag(z): if (z|type) == "number" then 0 else z[1] end;
+
+def plus(x; y):
+    if (x|type) == "number" then
+       if  (y|type) == "number" then [ x+y, 0 ]
+       else [ x + y[0], y[1]]
+       end
+    elif (y|type) == "number" then plus(y;x)
+    else [ x[0] + y[0], x[1] + y[1] ]
+    end;
+
+def multiply(x; y):
+    if (x|type) == "number" then
+       if  (y|type) == "number" then [ x*y, 0 ]
+       else [x * y[0], x * y[1]]
+       end
+    elif (y|type) == "number" then multiply(y;x)
+    else [ x[0] * y[0] - x[1] * y[1],
+           x[0] * y[1] + x[1] * y[0]]
+    end;
+
+def negate(x): multiply(-1; x);
+
+def minus(x; y): plus(x; multiply(-1; y));
+
+def conjugate(z):
+  if (z|type) == "number" then [z, 0]
+  else  [z[0], -(z[1]) ]
+  end;
+
+def invert(z):
+  if (z|type) == "number" then [1/z, 0]
+  else
+    ( (z[0] * z[0]) + (z[1] * z[1]) ) as $d
+   # use "0 + ." to convert -0 back to 0
+    | [ z[0]/$d, (0 + -(z[1]) / $d)]
+  end;
+
+def divide(x;y): multiply(x; invert(y));
+
+def exp(z):
+  def expi(x): [ (x|cos), (x|sin) ];
+  if (z|type) == "number" then z|exp
+  elif z[0] == 0 then expi(z[1])  # for efficiency
+  else multiply( (z[0]|exp); expi(z[1]) )
+  end ;
+
+def test(x;y):
+  "x =      \( x )",
+  "y =      \( y )",
+  "x+y:     \( plus(x;y))",
+  "x*y:     \( multiply(x;y))",
+  "-x:      \( negate(x))",
+  "1/x:     \( invert(x))",
+  "conj(x): \( conjugate(x))",
+  "(x/y)*y: \( multiply( divide(x;y) ; y) )",
+  "e^iπ:    \( exp( [0, 4 * (1|atan)  ] ) )"
+;
+
+test( [1,1]; [0,1] )

Task/Arithmetic-Complex/Jq/arithmetic-complex-2.jq

@@ -0,0 +1,10 @@
+$ jq -n -f complex.jq
+"x =      [1,1]"
+"y =      [0,1]"
+"x+y:     [1,2]"
+"x*y:     [-1,1]"
+"-x:      [-1,-1]"
+"1/x:     [0.5,-0.5]"
+"conj(x): [1,-1]"
+"(x/y)*y: [1,1]"
+"e^iπ:    [-1,1.2246467991473532e-16]"